cp's OEIS Frontend

A276639 Triangle T(m, n) = the number of point-labeled graphs with n points and m edges, no points isolated. By rows, n >= 0, ceiling(n/2) <= m <= binomial(n,2).

%I A276639 #25 Apr 15 2021 20:25:32
%S A276639 1,1,3,1,3,16,15,6,1,30,135,222,205,120,45,10,1,15,330,1581,3760,5715,
%T A276639 6165,4945,2997,1365,455,105,15,1,315,4410,23604,73755,159390,259105,
%U A276639 331716,343161,290745,202755,116175,54257,20349,5985,1330,210,21,1
%N A276639 Triangle T(m, n) = the number of point-labeled graphs with n points and m edges, no points isolated. By rows, n >= 0, ceiling(n/2) <= m <= binomial(n,2).
%C A276639 The row sums are A006129, omitting row 1 and A006129(1).
%H A276639 David Pasino, <a href="/A276639/b276639.txt">Table of n, a(n) for n = 1..512</a>
%F A276639 T(n, m) = Sum_{k=0,..n} binomial(n, k) * (-1)^(n-k) * A084546(k, m).
%e A276639 Triangle T(n, m) begins:
%e A276639 n/m  0  1  2  3   4    5    6    7    8    9   10
%e A276639 0    1  0  0  0   0    0    0    0    0    0   0
%e A276639 1    0  0  0  0   0    0    0    0    0    0   0
%e A276639 2    0  1  0  0   0    0    0    0    0    0   0
%e A276639 3    0  0  3  1   0    0    0    0    0    0   0
%e A276639 4    0  0  3  16  15   6    1    0    0    0   0
%e A276639 5    0  0  0  30  135  222  205  120  45   10  1
%t A276639 Table[Sum[Binomial[n, k] (-1)^(n - k) Binomial[Binomial[k, 2], m], {k, 0, n}], {n, 7}, {m, Ceiling[n/2], Binomial[n, 2]}] /. {} -> {1} // Flatten (* _Michael De Vlieger_, Sep 19 2016 *)
%Y A276639 Another version is A054548.
%K A276639 nonn,tabf
%O A276639 1,3
%A A276639 _David Pasino_, Sep 08 2016